How do I let my current employer down easy?

I'll try and make this as short as possible while providing as much perspective as I can:

I recently took a position (beginning of Dec) with a company that I have no complaints about so far. I was in a bit of a tight spot; I was the Director of Sales and Ops for a smaller company that decided to shutter my sector of their company to maximize profits in another, so I took this position knowing it was under my current level. Comp is fine; only slightly less than what I was making at my former company when you include monthly bonuses, etc.

A few weeks back, I was approached by a former colleague about a position with a company I've been trying to get on with for several years. Positions never come up for this company, as most people either are promoted or retire. Comp is a significant lift, as are benefits and the culture is well known to be an industry best. This position would provide a ton of stability, better comp, and better benefits all around. Additionally, it seems that I'm a frontrunner for the job, according to my former colleague.

Thing is, my current company is also great culture-wise, and they seem to be investing in moving me up quickly. It's a no-brainer for me to accept this position I'm moving through the interview process for if offered, but I really hate to let down the leadership team who seems to be investing big into me.

Any tips on the nicest possible way to let my current company down easy? I'm not a known "job-hopper"; My Director position was the shortest tenure I've had in my career, and even that was 3 years. I want my leadership team to know I wasn't looking and this opportunity was dropped in my lap, and had it not become an opportunity, I would not have been looking.

I've just never been in this position before, and I'd love input from this community.